article Yoav Len author Martin Ulirsch author 114697 Dmitry Zakharov author Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify harmonic $\mathfrak{A}$-covers of a tropical curve $Γ$ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on $Γ$. We give a realizability criterion for harmonic $\mathfrak{A}$-covers by patching local monodromy data in an extended homology group on $Γ$. As an explicit example, we work out the case $\mathfrak{A}=\mathbb{Z}/p\mathbb{Z}$ and explain how realizability for such covers is related to the nowhere-zero flow problem from graph theory. 2019 eng 1906.0421510.1017/S0305004123000518 Len, Yoav, et al. “Abelian Tropical Covers.” <i>ArXiv:1906.04215</i>, 2019, doi:<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>. Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. <i>arXiv:190604215</i>. Published online 2019. doi:<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a> @article{Len_Ulirsch_Zakharov_2019, title={Abelian tropical covers}, DOI={<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>}, journal={arXiv:1906.04215}, author={Len, Yoav and Ulirsch, Martin and Zakharov, Dmitry}, year={2019} } Len, Y., Ulirsch, M., &#38; Zakharov, D. (2019). Abelian tropical covers. <i>ArXiv:1906.04215</i>. <a href="https://doi.org/10.1017/S0305004123000518">https://doi.org/10.1017/S0305004123000518</a> Y. Len, M. Ulirsch, and D. Zakharov, “Abelian tropical covers,” <i>arXiv:1906.04215</i>, 2019, doi: <a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>. Y. Len, M. Ulirsch, D. Zakharov, ArXiv:1906.04215 (2019). Len, Yoav, Martin Ulirsch, and Dmitry Zakharov. “Abelian Tropical Covers.” <i>ArXiv:1906.04215</i>, 2019. <a href="https://doi.org/10.1017/S0305004123000518">https://doi.org/10.1017/S0305004123000518</a>. 663252026-07-08T06:50:59Z2026-07-08T08:22:44Z